You are here:

Calculus/Physics related Calc

Advertisement

Expert: - 9/6/2010


Question

Pulse train
Consider the periodic pulse train p(t) shown below where the
width of each pulse *delta* equals 0.2T. (The Pulse train
p(t) is formed when DC signal A is ON for a period *delta*
and OFF for a period T-*delta* and so on.  In this regard
*delta* is called the duty period.)
Complete the integrals with the details leading to the
answer provide

The average value of p(t)= (1/T) integral (p(t)dt) [T,0]
= A/5

The RMS value of p(t)= ((1/T)integral (p^(2)(t)dt) [T,0]

Answer
Hi Janisa,
p(t) = A (from t = 0 to Δ)
and 0 (from t = Δ to T)
The mean value of p(t) = (1/T) ∫p(t) dt  (from 0 to T)
= (1/T) [∫p(t) dt  (from 0 to Δ) + ∫p(t) dt  (from Δ to T)]
= (1/T) [∫A dt  (from 0 to Δ) + ∫0 dt  (from Δ to T)]
= (1/T) [At  (from 0 to Δ) + 0  (from Δ to T)]
= (1/T) [(A.Δ - A.0) + (0.T - 0.Δ)]
= (1/T)(A.Δ)
= AΔ/T
= A(0.2T)/T
= 0.2A
= A/5

The root-mean-square value of p(t) = √[(1/T) ∫p(t) dt]  (from 0 to T)
= √(1/T) [∫p(t)² dt  (from 0 to Δ) + ∫p(t)² dt  (from Δ to T)]
= √(1/T) [∫A² dt  (from 0 to Δ) + ∫0² dt  (from Δ to T)]
= √(1/T) [A²t  (from 0 to Δ) + 0  (from Δ to T)]
= √(1/T) [(A².Δ - A².0) + (0.T - 0.Δ)]
= √(1/T)(A².Δ)
= √(A²Δ/T)
= √A²(0.2T)/T
= √(0.2A²)
= A√0.2
= A/√5
= (A√5)/5

Regards

Ahmed Salami

Expertise

I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I believe i would be very helpful in calculus and can as well help a good deal in Physics with most emphasis directed towards mechanics.

Experience

An engineering graduate. I have been doing maths and physics all my life.

©2012 About.com, a part of The New York Times Company. All rights reserved.